Estimation of the soluble solid content of citrus based on the fractional-order derivative and optimal band combination algorithm

The soluble solid content (SSC) is a primary characteristic index for evaluating the internal quality of citrus fruits. The development of rapid and nondestructive SSC detection techniques can help address the current issues of postharvest quality grading in China's citrus industry. In this study, a total of 261 experimental samples, including 70 Murcott, 91 Clementine, and 100 Navel orange, were divided into prediction and validation sets in a 7:3 ratio. After obtaining the reflection spectra and SSCs, SNV-FOD (Standard Normal Variate-Fractional-Order Derivative) was used to process the spectra, and the optimal band combination algorithm was introduced to select SSC-sensitive bands. Then, the obtained optimal dual-band combination was input into eight regression models for comparison, and the best performing models stacked ensemble models was selected. Finally, the H-ELR (HyperOpt-optimized ensemble learning regression) model, optimized using a Bayesian function, was applied for the effective estimation of SSC for three common citrus varieties in Guangxi, Murcott, Clementine, and Navel oranges. The results show that (1) the SNV-FOD preprocessing method proposed in this study improved the correlation coefficient with the SSC from 0.546 to 0.836 compared to that of the original spectrum, (2) the optimal dual-band combination (969 and 1069 nm) constructed by integrating the differential index and 1.2-order derivative yielded the most accurate results (RPD = 2.13), and (3) the H-ELR model, based on HyperOpt optimization, achieved good estimated performance (RPD = 2.46).